If you get some compiling errors when using babel@^7.0.0, that's because Vuepress is using babel's beta version now, maybe some dependencies are not compatible with your babel's version, you can fix it by adding resolutions in package.json, eg:
{
"resolutions": {
"vuepress/**/@babel/preset-stage-2": "7.0.0",
"vuepress/**/@babel/core": "7.4.4",
"vuepress/**/@babel/runtime": "7.4.4",
"vuepress/**/babel-loader": "8.0.6",
"vuepress/**/@vue/babel-preset-app": "3.3.0"
}
}